One of the biggest challenges in selecting a font for TeX or LaTeX
is that there are not very many math fonts that match the plethora
of available text fonts. It's reasonably easy to use an arbitrary
Postscript Type 1 font in TeX for text (see Philipp Lehman's Font
Installation Guide [1]), but obtaining and configuring
a matching math font from scratch is a demanding task. Thus, there
are few math fonts for TeX, and in particular very few free ones.
However, in the past few years, several very nice free fonts have
been released. The goal of this article is to list all of the free
math fonts and to provide examples.

“Free” here means fonts that are free to use (both commercially
and non-commercially) and free to distribute, but not necessarily
free to modify. I also am biased towards listing fonts that have outline
versions in PostScript Type 1 format suitable for embedding in Postscript
PS or Adobe Acrobat PDF files. Donald E. Knuth originally designed
the METAFONT system for producing fonts for TeX in bitmap format.
PS or PDF files that have embedded bitmap fonts do not display well
in Adobe Acrobat Reader,3 to the point of being almost unreadable on the screen, and are also
noticeable when printing at extremely high resolutions (on photo-setters,
for instance). Since outline fonts contain mathematical descriptions
of the curves used in each glyph, they can be scaled to any resolution
while retaining image quality.

The fonts listed here are categorized according to their origin: whether
originally designed for TeX, related to the standard Postscript
fonts, or other free fonts. A font's origin does not particularly
bear on its quality or suitability for typesetting mathematics. No
recommendations or evaluations of the fonts are given here, as people's
tastes in fonts vary greatly. The goal of this survey is simply to
make authors aware of all their options.

Most of the fonts can be selected by including a single package in
the preamble of the user's LaTeX file (the preamble is the
section after “\documentclass{}” and
before “\begin{document}”). The line
or lines to include for each font are listed in the caption of the
sample figure. For example “\usepackage{fourier}”
uses Utopia and Fourier-GUTenberg, as shown in the sample LaTeX
file in Section 6.

Walter A. Schmidt also has a survey in German of math fonts [3]
that concentrates more on commercial fonts. Schmidt's survey has several
examples that show different pairings between text fonts and math
fonts.

These fonts were originally designed for use with TeX, using either
METAFONT or MetaType1 [2].

Computer Modern:

Knuth created Computer Modern [5] as the default font
for TeX. The font set includes serif, sans serif, and monospaced
text faces, and corresponding math fonts. The math symbol set is very
complete. Computer Modern is the font for TeX, which leads
some to claim that the font is overused. The characters are fairly
thin and light, and so are not as readable on screen in small sizes
or from high-resolution laser printers.4 In a comparison by Raph Levien [6], the printing in
Knuth's Digital Typography [7] is heavier than
the digital version or from a laser printer.

Type 1 versions of Computer Modern from Blue Sky Research and Y&Y,
Inc. have been made freely available by the American Mathematical
Society (AMS) and a collection of publishers and other technical companies [8, 4].
Basil K. Malyshev has also released a free Type 1 version of Computer
Modern [9], originally for use with his TeX system
BaKoMa TeX.

Computer Modern has been extended to include more characters, particularly
for non-English European languages. These fonts include European Computer
Modern by Jörg Knappen and Norbert Schwarz (METAFONT only) [10];
Tt2001 by Szabó Péter (converted into Type 1 format from METAFONT
sources using textrace; Tt2001 has been superseded by CM-Super,
which Péter recommends) [12, 11]; CM-Super by
Vladimir Volovich (also converted using textrace) [14, 13];
and Latin Modern by Bogusław Jackowski and Janusz M. Nowacki (extended
from the Blue Sky AMS fonts using MetaType1) [16, 15].

The SliTeX font (lcmss) is a sans serif text face that
has wide letters and high x height. Its high readability makes
it extremely suitable for slide presentations. However, there is no
matching math font. SliTeX sans serif can be set as the primary
text font using TeXPower's tpslifonts.sty [17].

Computer Modern Bright:

This a sans serif font with corresponding math font derived from Computer
Modern by Walter A. Schmidt [18]. CM-Super contains
Type 1 versions of the text fonts in T1 encoding, and Harald Harders
created Type 1 versions of the text and math fonts called hfbright [19]
using mftrace.

Concrete and Euler or Concrete Math:

The Concrete font was created by Knuth for his book Concrete
Mathematics [20]. Hermann Zapf was commissioned
by the AMS to create the math font Euler for use in Concrete
Mathematics. Type 1 versions of Concrete in T1 encoding are available
in the CM-Super collection [13], and Type 1 versions
of Euler are available in the Blue Sky collection from the AMS [8]
and in the BaKoMa collection [9]. The eulervm
package by Walter Schmidt [23, 24] implements
virtual fonts for Euler that are more efficient to use with LaTeX.
Ulrik Vieth created the Concrete Math fonts [21]
to match the Concrete text fonts; the only free versions are implemented
in METAFONT. The ccfonts package by Walter Schmidt [22]
changes the text font to Concrete and changes the math font to the
Concrete Math fonts if eulervm is not loaded.

Figure 3: Concrete
text with Euler math (\usepackage{ccfonts,eulervm}
\usepackage[T1]{fontenc}). Note that Concrete
does not have a bold font, so Computer Modern is used instead. Non-bold
text output uses the CM-Super Concrete fonts.

Figure 4: Concrete text with
Concrete math (\usepackage{ccfonts} \usepackage[T1]{fontenc}).
Note that Concrete does not have a bold font, so Computer Modern is
used instead. Non-bold text output uses the CM-Super Concrete fonts.

Iwona and Kurier:

The fonts Iwona and Kurier were created by J. M. Nowacki [25, 26]
using the MetaType1 system based on typefaces by the Polish typographer
Małgorzata Budyta. The two fonts are very similar, except that
Kurier avoids “ink traps” with gaps in its strokes. The packages
have complete math support in both TeX and LaTeX.

Figure 5: Iwona text and math (\usepackage[math]{iwona}).

Figure 6: Kurier text and math (\usepackage[math]{kurier}).

Antykwa Półtawskiego:

J. M. Nowacki created the font Antykwa Półtawskiego [27]
using the MetaType1 system based on a typeface by Polish typographer
Adam Półtawski. The package antpolt has no math support
at this time, and requires the encoding to be set to QX or OT4.

Antykwa Toruńska:

The font Antykwa Toruńska was created by J. M. Nowacki [29, 28]
using the MetaType1 system based on a typeface by the Polish typographer
Zygfryd Gardzielewski. The package anttor has complete math
support in both TeX and LaTeX.

When Adobe introduced Postscript in 1984, they defined 35 core fonts
(in 10 typefaces) that must be present in all Postscript interpreters.
In 1996, URW++ released a replacement set for the core fonts under
the GNU General Public License. The URW++ fonts were primarily released
for use with Ghostscript, a free Postscript interpreter. Table 1
lists the original Postscript fonts, along with the URW++/Ghostscript
equivalents. Each font can be used as the default text font by selecting
the indicated LaTeX package from the PSNFSS distribution [30].

Adobe Postscript

URW++/Ghostscript

# of fonts

package

Avant Garde

URW Gothic L

4

avant

Bookman

URW Bookman L

4

bookman

Courier

Nimbus Mono L

4

courier

Helvetica

Nimbus Sans L

8

helvet

New Century Schoolbook

Century Schoolbook L

4

newcent

Palatino

URW Palladio L

4

palatino

Symbol

Standard Symbols L

1

—

Times

Nimbus Roman No. 9 L

4

times

Zapf Chancery

URW Chancery L

1

chancery

Zapf Dingbats

Dingbats

1

—

Table 1: Core
Postscript fonts and URW++/Ghostscript equivalents.

Avant Garde and Kerkis Sans:

The font Kerkis Sans was created by Antonis Tsolomitis [31, 32]
by extending Avant Garde to include Greek and additional Latin characters.
The resulting fonts are stand-alone and can be used by applications
outside of TeX. The package kerkis sets the sans serif
font to Kerkis Sans; there is no package option to set Kerkis Sans
to be the primary text font.

Bookman and Kerkis:

The font Kerkis was created by Antonis Tsolomitis [31, 32]
by extending URW Bookman L to include Greek and additional Latin
characters. The resulting fonts are stand-alone and can be used by
applications outside of TeX. A font of math symbols is included,
but not used by the LaTeX package. The package kmath uses
txfonts for math symbols and uppercase Greek letters.

Figure 9: Kerkis text and math (\usepackage{kmath,kerkis};
the order of the packages matters, since kmath loads the
txfonts package which changes the default text font).

New Century Schoolbook and Millennial or fouriernc:

The Millennial math font of the current author contains Greek letters
and other letter-like mathematical symbols. A set of virtual fonts
is provided that uses New Century Schoolbook for Latin letters in
math, Millennial for Greek and other letter-like symbols, and txfonts
and Computer Modern for all other symbols, including binary operators,
relations, and large symbols. This font is still in development, but
will hopefully be released in 2006. The fouriernc package
of Michael Zedler [33] uses New Century Schoolbook
for text and Latin letters in mathematics, and the Greek and symbol
fonts from the Fourier-GUTenberg package for the remaining mathematical
symbols.

Figure 10: New Century Schoolbook
with Millennial math (\usepackage{millennial}).

Figure 11: New Century Schoolbook
with Fourier math (\usepackage{fouriernc}).

Palatino and pxfonts, Pazo, or mathpple:

Young Ryu created the pxfonts collection [34], which
contains Greek and other letter-like symbols, as well as a complete
set of geometric symbols, including the AMS symbols. Diego Puga created
the Pazo math fonts, which include the Greek letters and other letter-like
symbols in a style that matches Palatino. The LaTeX package mathpazo
(now part of PSNFSS [30]) uses Palatino for Latin letters,
Pazo for Greek and other letter-like symbols, and Computer Modern
for geometric symbols. The LaTeX package mathpple (also
part of PSNFSS [30]) uses Palatino for Latin letters
and slanted Euler for Greek and other symbols. Since Hermann Zapf
designed both Palatino and Euler, the designs mesh well. An alternate
use of Euler is using the eulervm package. Ralf Stubner added
small caps and old-style figures to URW Palladio L in the FPL package [36],
and Walter Schmidt extended these fonts in the FPL Neu package [37].

Figure 12: Palatino text with pxfonts
math (\usepackage{pxfonts}).

Figure 13: Palatino text with Pazo math
(\usepackage{mathpazo}).

Figure 14: Palatino text with Euler
math (\usepackage{mathpple}).

Times and txfonts, Belleek, mathptmx, or mbtimes:

Young Ryu created the txfonts collection [38], which
contains Greek and other letter-like symbols, as well as a complete
set of geometric symbols, including the AMS symbols. The txfonts
package also includes a very nice typewriter font, txtt.
Belleek was created by Richard Kinch [39, 40]
and is a drop-in replacement for the commercial fonts required by
the mathtime package (now part of PSNFSS [30]).
The LaTeX package mathptmx (also part of PSNFSS [30])
uses Times for Latin letters and Symbol for Greek and other symbols.
Michel Bovani created the mbtimes package by using Omega
Serif for text and Latin and Greek letters in mathematics. mbtimes
also includes symbol fonts and a set of calligraphic letters. Omega
Serif is the primary font for Omega, a 16-bit extension of TeX
by John Plaice and Yannis Haralambous [43].

The STIX fonts project [41] is a collaboration of several
academic publishers to create a set of Times-compatible fonts containing
every possible glyph needed for mathematical and technical publishing.
These fonts are still in development, with a scheduled release in
the middle of 2006.

Note that Adobe Reader 7.0 replaces Times with Adobe Serif MM if Times
or the Ghostscript equivalent Nimbus Roman No. 9 L is not embedded
in the PDF file. Adobe Serif MM only has an oblique version, not a
real italics, and thus, the primary text and Latin letters in mathematics
will not match letters taken from additional fonts. This problem can
be avoided by embedding Times or the Ghostscript equivalent Nimbus
Roman No. 9 L into the PDF file. Also, I have heard (but not personally
verified) that the Windows version of Adobe Reader displays Times
New Roman when Times is not embedded. The upright versions of the
two typefaces are very similar, but the italics are noticeably different
(consider the z, for instance).

Helvetica, Courier, and Zapf Chancery do not have matching math fonts.
Courier and Zapf Chancery are inappropriate for mathematics anyway,
but Helvetica is sometimes used for presentations and posters. The
free fonts MgOpenModerna [44] and FreeSans [45]
would be natural choices for the Greek letters in a Helvetica mathematics
font.

Several other fonts have been released for use with free open-source
software. LaTeX packages have been created for most of these fonts.

Bitstream Vera Sans and Arev Sans:

Bitstream Vera was released by Bitstream in cooperation with the Gnome
Foundation [46] as a high quality scalable free font for
use with free open-source software. Bitstream Vera serif, sans serif,
and sans mono are available in text using the bera package
by Malte Rosenau and Walter A. Schmidt [47]. Tavmjong
Bah created Arev Sans [49] by extending Bitstream Vera Sans
to include Greek, Cyrillic, and many mathematical symbols. The current
author created the LaTeX package arev [48]
using Arev Sans for text and math letters and bold Math Design fonts
for Bitstream Charter for symbols.

Figure 19: Arev Sans text with Arev
math (\usepackage{arev}).

Bitstream Charter and Math Design:

Bitstream Charter [50] was donated by Bitstream for
use with X Windows. The Math Design fonts for Bitstream Charter created
by Paul Pichaureau [51] are very complete, including
Greek letters, symbols from Computer Modern, and the AMS symbols.
Charis SIL [52] might be an alternate source for Greek
letters that match Bitstream Charter more closely. Another possibility
for a math font is to use the Euler fonts with the charter
and eulervm packages.

Comic Sans:

Comic Sans is one of Microsoft's core web fonts that is freely available [53].
The comicsans package by Scott Pakin [54]
implements Comic Sans as both the primary text font and the Latin
and Greek letters in mathematics. Computer Modern is used for geometric
symbols that are not present in Comic Sans. Comic Sans is hard to
read for large blocks of text, but might be nice to use for short
comments in a handwriting style.

Figure 21: Comic Sans text and
math (\usepackage{comicsans}).

URW Garamond and Math Design:

URW Garamond No. 8 [55] is available under the Aladdin
Free Public License as part of the GhostPCL project. The Math Design
fonts for URW Garamond created by Paul Pichaureau [51]
are very complete, including Greek letters, symbols from Computer
Modern, and the AMS symbols.

Utopia and Fourier or Math Design:

Utopia [56] was donated by Adobe for use with X Windows.
Michel Bovani created Fourier-GUTenberg [57] as an
accompaniment to Utopia and is very complete, containing both Greek
letters and standard and AMS symbols. The Math Design fonts for Utopia
of Paul Pichaureau [51] are also very complete,
including Greek letters and AMS symbols.

Table 2 shows a comparison of the different
features in each package. The only packages that have optical sizes
are Computer Modern, CM Bright, Concrete, Euler, and MnSymbol. Except
for when the eulervm package is used, Latin math letters
are taken from the italic text font. An asterisk after a font name
indicates that the package has a version of that style in its own
font files.

Package

Text

Greek

CM sym

AMS sym

Calligr

Blkbd

boldmath

computer modern

cm

cm

cm

ams

cm

ams

yes

cmbright

cmbright

cmbright

cm*

cm*

cm*

ams

no

ccfonts,eulervm

concrete

euler

euler

ams

euler

ams

yes

concmath

concrete

concrete

concmath

concmath

concmath

concmath

no

iwona

iwona

iwona

iwona

iwona

cm*

ams

yes

kurier

kurier

kurier

kurier

kurier

cm*

ams

yes

anttor

anttor

anttor

anttor

anttor

anttor

ams

yes

kmath,kerkis

kerkis

kerkis

txfonts

txfonts

txfonts

txfonts

yes

millennial

nc schlbk

millennial

txfonts

txfonts

txfonts

ams

no

fouriernc

nc schlbk

fourier

fourier

fourier

fourier

fourier

yes

pxfonts

palatino

pxfonts

txfonts*

txfonts*

txfonts*

pxfonts

yes

mathpazo

palatino

pazo

cm

ams

cm

pazo

yes

mathpple

palatino

euler

euler

ams

cm

ams

yes

txfonts

times

txfonts

txfonts

txfonts

txfonts

txfonts

yes

mathtime (Belleek)

times

belleek

belleek

ams

cm

ams

no

mathptmx

times

symbol

cm

ams

rsfs

ams

no

mbtimes

omega

omega

mbtimes

ams

rsfs*

esstix

yes

arev

arev

arev

md charter

md charter

cm

fourier

yes

mathdesign (Charter)

charter

md charter

md charter

md charter

rsfs*

ams

yes

comicsans

comicsans

comicsans

cm

cm

cm

cm

yes

mathdesign (Garamond)

garamond

md garamond

md garamond

md garamond

rsfs*

ams*

yes

fourier

utopia

fourier

fourier

fourier

fourier

fourier

yes

mathdesign (Utopia)

utopia

md garamond

md utopia

md utopia

rsfs*

ams*

yes

Table 2: Comparison
of the features of different packages.

The only sans serif fonts with matching math fonts are CM Bright and
Arev Sans. Both work well for presentations. Computer Modern sans
serif, CM Bright, Arev Sans, Bera Sans, Kerkis Sans, Helvetica, and
Avant Garde all work well as sans serif fonts that accompany a primary
roman font. Computer Modern typewriter, txtt (from txfonts),
Luxi Mono [61], and Bera Mono all work well as typewriters
fonts.

There are several other free fonts easily used in LaTeX, notably
the Bera fonts, Luxi Mono, and efont-serif [62]. Malte
Rosenau converted the Bitstream Vera fonts into Type 1 format, renaming
the fonts to Bera [47]. Bera includes serif, sans, and
mono. Bera Serif does not have a matching italic font, but the DejaVu
fonts [60] are an extension of Bitstream Vera that include
a true serif italic, as well as Greek and Cyrillic for all three styles.
Except for Bera Sans and Arev Sans, none of the previous fonts have
matching math fonts.

It might be technically feasible to create a font survey such as this
article as a single TeX document. This document, however, was not
created in that fashion for two reasons. First, it would be an inordinate
amount of work to switch between fonts within the same document. The
authors of the LaTeX packages put in a considerable amount of effort
to set up the fonts for a document, and it would be silly to duplicate
their work. Second, we want to show to a reader exactly what he or
she will get by using that package.

In order to accomplish these goals, a small LaTeX file (see Figure 25
for an example) was made for each font that loaded the appropriate
packages and then loaded a common text fragment for display. Each
file was LaTeXed and then converted to an EPS file using dvips
with the -E option. The -E option creates a tight bounding box around
the text. The main file survey.tex then included each of
these graphics, and was compiled with pdflatex. For some
reason, dvips created an unusable one-page PS file when including
mbtimes.eps. HeVeA was used to convert survey.tex
directly to HTML.

Figure 25: Sample
LaTeX file for fourier. The file sampleformat.tex
contains page layout commands, such as setting the margins and removing
the page numbers. The file textfragment.tex contains the
text and mathematics fragment to be displayed. Both included files
are used by every sample LaTeX file. The line “\usepackage{fourier}”
was changed for each sample to the package listed in the sample's
caption.

When on screen, the fonts are usually anti-aliased, often into a gray
blur because the stems are not thick enough to fill a pixel. When
printed with a high-resolution laser printer, the fonts are shown
accurately, but I think are too thin. With a medium-resolution printer
like an inkjet, there's enough resolution to show the form of the
letters (unlike on screen), but the low-resolution "bulks
up" the letters compared to a high-resolution laser printer,
with the letters thus appearing darker.